Abstract
We generalize the theory of Nash-Williams on well quasi-orders and better quasi-orders and later results to uncountable cardinals. We find that the first cardinal κ for which some natural quasi-orders are κ-well-ordered, is a (specific) mild large cardinal. Such quasi-orders are
(the class of orders which are the union of ≦λ scattered orders) ordered by embeddability and the (graph theoretic) trees under embeddings taking edges to edges (rather than to passes).
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This research was supported by the United States-Israel Binational Science Foundation, grant 1110.
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Shelah, S. Better quasi-orders for uncountable cardinals. Israel J. Math. 42, 177–226 (1982). https://doi.org/10.1007/BF02802723
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DOI: https://doi.org/10.1007/BF02802723